The OOD detection is a binary classification problem, which outputs a score \(s_{\mathbf {\theta }}(\mathbf {x}) \in \mathbb {R}\)  for a given query \(\mathbf {x}\) . The model should be able to assign lower scores to OOD examples than to in-distribution examples, such that it can be used to distinguish two sets of examples. Following the settings of JEM [1]}, we use the Area Under the Receiver-Operating Curve (AUROC) [2]} to evaluate the performance of OOD detection. In our experiments, three score functions are considered: the input density \(p_{\mathbf {\theta }}(\mathbf {x})\)  [3]}, the predictive distribution \(p_{\mathbf {\theta }}(y|\mathbf {x})\)  [2]}, and the approximate mass \(\Vert  \frac{\partial \log p_{\mathbf {\theta }}(\mathbf {x})}{\partial \mathbf {x}}\Vert \)  [1]}.
